Problem: Determine how many solutions exist for the system of equations. ${-5x-y = 6}$ ${-4x+y = -4}$
Convert both equations to slope-intercept form: ${-5x-y = 6}$ $-5x{+5x} - y = 6{+5x}$ $-y = 6+5x$ $y = -6-5x$ ${y = -5x-6}$ ${-4x+y = -4}$ $-4x{+4x} + y = -4{+4x}$ $y = -4+4x$ ${y = 4x-4}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -5x-6}$ ${y = 4x-4}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.